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Register a new userShort- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow
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Added by
Rodolphe Chabreyrie
Publication date
2014
fields
Physics
and research's language is
English
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Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincare section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.
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Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. Turbulent flows promote efficient transport and mixing by their inherent randomness. Laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion (`advection) and the geometry, topology and coherence of fluid trajectories. Efficient laminar transport being equivalent to `chaotic advection is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows yet the real world is three dimensional (3D). Second, Lagrangian transport is typically investigated for idealised flows yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilisation of know-how on 3D Lagrangian transport and its dissemination to practice. To this end 3D practical flows are categorised into canonical problems. First, to expose the diversity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the `Lagrangian mindset into the analysis and design of 3D practical flows.
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The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modelled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions amongst inertial beads result in a non-trivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, non-interacting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (2018)]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly-inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.
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